Where will my state return will be? Will I get it like my federal’s? On ny bank with direct deposit?

How you chose to receive the state tax refund will be on the Filing Instructions page for the state return.

To access your current or prior year online tax returns sign onto the TurboTax website with the User ID you used to create the account - https://myturbotax.intuit.com/

When you sign onto your online account and land on the Tax Home web page, scroll down and click on Add a state. 

This will take you back to the 2023 online tax return.

Click on Tax Tools on the left side of the online program screen.  Then click on Print Center.  Then click on Print, save or preview this year's return.

Unless you told TurboTax to send your state refund somewhere else, it will go to the same account that your federal did.   You can check the status at your state's department of revenue.